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The spurious velocity is the unphysical circulating velocity near
the interface. The presence will affect the accuracy of the
simulation and also cause numerical stability problems. This
phenomenon is a common problem for many other multiphase simulations
like VOF , color gradient LBM and free energy LBM. The magnitude is
found related with the width of the interface and the surface
tension. Increased surface tension will lead to big spurious
velocity while wider interface gives smaller spurious velocity. The
existence of spurious limited ability of the pseudo potential model
to simulate high density ratios or low viscosities. Shan (2008)
reported that the spurious is due to the lack of sufficient isotropy
in the calculation of the gradient term for force. Finite difference gradient of force with higher degree of isotropy
is also introduced.\\

Long-range intermolecular interaction can be introduced by defining
a interaction potential between neighboring site:

\begin{equation}
V(x,x')=G(x,x')\psi (x) \psi (x')
\end{equation}

Where $\psi=\psi(\rho)$ is the "effective mass" that defines the
details of the interparticle interaction. The force can be obtained
by

\begin{equation}
F=-G(|e_a|)\psi(x) \sum\limits_a \psi (x+e_a)e_a
\end{equation}


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